Principles of Fluorescence Spectroscopy

482 TIME-RESOLVED ENERGY TRANSFER AND CONFORMATIONAL DISTRIBUTIONS OF BIOPOLYMERS
additional data. During this fit the mean distance was a variable
parameter. For the flexible peptide TrpNH 2 –(gly) 6 –
DNS the alternative model was tested by attempting to fit
the data using the half width of 4 Å found for the rigid peptide.
The value of hw = 4 Å is held constant and the leastsquares
fit run again to minimize χ R 2 using the flexible peptide
data. The dashed line (Figure 14.7, left) shows the data
for TrpNH 2 –(gly) 6 –Gly are not consistent with a narrow
distance distribution. Similarly, the data for TrpNH 2 –
(pro) 6 –DNA could not be fit with a wide distribution
(dashed line, curves in right panel of Figure 14.7). In these
cases the attempt to fit the data with different parameter values
resulted in obviously unacceptable fits. However, for
conformational changes of proteins one can expect the distance
distributions to be more similar than for these two
hexapeptides, so that the ability to reject similar distributions
may be more questionable.
14.2.3. Donor Decay without Acceptor
An important aspect of the distance-distribution analysis is
knowledge of the donor decay time. This is typically measured
using a control molecule that is comparable to the
D–A pair except that it lacks the acceptor (donor-alone molecule).
In the case of the two hexapeptides the donor control
molecule was TrpNH 2 –(gly) 3 –Ac, in which the tryptophan
donor was attached to a glycine tripeptide. The tripeptide
was acetylated at the N terminus to be more like the
D–A pairs and to avoid quenching by the terminal amino
group. The amide group does not quench the nearby indole.
The selection of a suitably designed donor-alone control
molecule is a critical step in any energy transfer experiment.
Typically the donor decay time (or decay times for a
multi-exponential decay) is measured separately. The data
(TD or FD) for the D–A pair are then analyzed while the
value of τ D is held fixed. This is necessary because the
donor intensity decays of the D–A pair only provides information
when compared to the decay that would be observed
without energy transfer.
Depending upon the available software the data for the
donor-alone and D–A pairs can also be analyzed simultaneously.
In this case the program needs to know that the
value(s) of τ D is determined only by the donor-alone data,
as there is no RET in the donor-alone decay. At first glance
one may think that this simultaneous analysis is identical to
fixing τ D , and analyzing the data for the D–A pair. In fact,
these two methods are different and this second analysis is
preferred. If the presence of the acceptor has no effect on
the donor decay besides that due to RET, both modes of
analysis will yield the same value of τ D . However, if the
presence of the acceptor somehow affects τ D other than by
RET, then the second mode of analysis could reveal this
effect. Alternatively, since energy transfer decreases the
intensity of the donor, an increased contribution of impurity
fluorescence to the data for the D–A pair could result in
different values of τ D for each mode of analysis.
14.2.4. Effect of Concentration of the D–A Pairs
In general, the extent of energy transfer depends on the concentration
of the D–A pairs. However, for linked D–A pairs
energy transfer is usually dominated by the linked acceptor.
For unlinked D–A pairs the acceptor concentration needs to
typically be in the millimolar range for significant energy
transfer (Chapter 15). This is because mM concentrations
are needed to result in one or more acceptor molecules to be
within the Förster distance of the donor. Hence, we made no
mention of the concentration of the linked D–A pairs in the
preceding sections. Knowledge of the concentration was
unnecessary because each donor sees an effective constant
concentration of the acceptor determined by the length and
flexibility of the linker to which the acceptor is attached.
However, the concentration of linked D–A pairs should be
low enough to avoid inner filter effects and transfer between
donors and acceptors on unlinked D–A pairs. Under these
conditions, the extent of energy transfer will be independent
of the bulk concentration of the D–A pairs.
14.3. DISTANCE DISTRIBUTIONS IN PEPTIDES
The principles described above have been applied to a wide
variety of proteins using time or frequency-domain measurements.
Time-domain measurements have been used to
recover distance distributions in native and unfolded
staphylococcal nuclease, 4 troponin C, 8 and cardiac troponin
I. 9 This approach was initially described by Haas and
coworkers on bovine pancreatic trypsin inhibitor (BPTI).
This protein was labeled with a naphthalene donor at the Nterminal
amino group, and selectively labeled with a
coumarin acceptor on each of its four lysine residues. The
labeled BPTI was studied during folding and unfolding to
determine the folding pathway. (See Representative Publications
on Measurement of Distance Distributions near the
end of this chapter for references). Frequency-domain
measurements have also been used to measure distance distributions
in proteins, including the ribonuclease S pep-